The MHD Caustic test is taken from [1]} which generalizes the HD test of [2]}. The initial sinusoidal velocity field in the x-direction has the peak value \(1/2\pi \) , the initial density and pressure has been set to be uniform with \(\rho =1\)  and \(p=10^{-10}\) . Then caustics will be formed because of the compression by the velocity field. An initial uniform magnetic field of \(10^{-3}\)  in code units in the y direction was added to the simulation. Figure REF  compares the density and \(B_y\)  at \(t=3\)  of unigrid and AMR runs. AMR run had 256 cells in the root grid and 2 level refinements by 2. The AMR solution is indistinguishable from a uniform grid solution with 1024 cells.
